Finite Group Databasebeta

← #11807613

Subgroups — #11807613

Order 1152.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1043 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63922C211yesmaximal, characteristic
2#10592369C211yesmaximal, characteristic, complemented
3C3×#4669C211yesmaximal, characteristic, complemented
4C3×#4665C211yesmaximal, characteristic, complemented
5#10591399C211yesmaximal, characteristic, complemented
6#10591399C211yesmaximal, characteristic, complemented
7#10591385C211yesmaximal, characteristic, complemented
8#10591384C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591318C211yesmaximal, characteristic, complemented
12#10591316C211yesmaximal, characteristic, complemented
13#10591283C211yesmaximal, characteristic, complemented
14#10591282C211yesmaximal, characteristic, complemented
15#10591202C211yesmaximal, characteristic, complemented
16#75840—31nomaximal
17#74882—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic, complemented
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
27C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C2×C3×C4×Dic3C2211yescharacteristic, complemented
36C2×#3724C2211yescharacteristic, complemented
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×Dic32C2211yescharacteristic, complemented
47#63922C418yescomplemented
48C32×#95C2211yescharacteristic, complemented
49#63658C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51C3×C3⋊#95C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54C2×#937—31no—
55C2×#882—31no—
56C3×#388—31no—
57C3×#386—31no—
58#5221—31no—
59#5213—31no—
60#5213—31no—
61#4990—31no—
62#4988—31no—
63#4957—31no—
64#4957—31no—
65#4957—31no—
66#4956—31no—
67#4955—31no—
68#4955—31no—
69#4955—31no—
70#4955—31no—
71#4951—31no—
72#4945—31no—
73#4945—31no—
74#4940—31no—
75#4939—31no—
76#4670—31no—
77#4670—31no—
78#4670—31no—
79#4670—61no—
80#4669—31no—
81#4669—31no—
82#4669D311yescharacteristic, complemented
83#4665—31no—
84#4665D311yescharacteristic, complemented
85C23×C3⋊D3C2311yescharacteristic
86C23×C3×D3C2311yescharacteristic
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×D32—41no—
90C22×D32—41no—
91C22×D32—41no—
92C22×D32—41no—
93C22×D32—41no—
94C22×D32—41no—
95C22×D32C2×C414yescomplemented
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×D12—41no—
108C2×C3×D12—41no—
109C2×C3×D12C2×C414yes—
110C2×C3×C4×D3—41no—
111C2×C3×C4×D3—41no—
112C2×C3×C4×D3—41no—
113C2×#626—41no—
114C2×#626—41no—
115C2×#626C2×C414yes—
116C2×#625—41no—
117C2×#625—41no—
118C2×#625C2×C414yes—
119#3752—41no—
120#3752—41no—
121#3752C2×C414yescomplemented
122C4⋊(C3⋊Dic3)—41no—
123C4×C3⋊Dic3—41no—
124C3×(C2×D3)⋊C4—41no—
125C3×(C2×D3)⋊C4—41no—
126C3×(C2×D3)⋊C4—41no—
127C3×(C2×D3)⋊C4—41no—
128C3×(C2×D3)⋊C4—41no—
129C3×(C2×D3)⋊C4C2×C414yescomplemented
130C3×Dic3⋊C4—41no—
131C3×C4×Dic3—41no—
132#3724—41no—
133#3722—41no—
134#3722—41no—
135(C2×D3)⋊Dic3—41no—
136(C2×D3)⋊Dic3—41no—
137(C2×D3)⋊Dic3—41no—
138(C2×D3)⋊Dic3—41no—
139(C2×D3)⋊Dic3—41no—
140(C2×D3)⋊Dic3—41no—
141(C2×D3)⋊Dic3C2×C414yescomplemented
142Dic32—41no—
143#2375—91noSylow
144C24×D3—31no—
145C24×D3—31no—
146C22×C3×D4—31no—
147C23×C3×C4—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×D12—31no—
152C22×D12C2×D311yescharacteristic
153C22×C4×D3C2×D311yescharacteristic, complemented
154C2×C3×C4⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C22⋊C4—31no—
158C2×C3×C22⋊C4—31no—
159C2×C3×C22⋊C4—31no—
160C2×C3×C22⋊C4—31no—
161C2×C3×C42—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165C2×#217—31no—
166C2×#217—31no—
167C2×#217—31no—
168C2×#217—31no—
169#937—38no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4—31no—
172C2×(C2×D3)⋊C4—31no—
173C2×(C2×D3)⋊C4—31no—
174C2×(C2×D3)⋊C4—31no—
175C2×(C2×D3)⋊C4—31no—
176C2×(C2×D3)⋊C4—31no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—61no—
188C2×(C2×D3)⋊C4—61no—
189C2×(C2×D3)⋊C4—61no—
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194C2×(C2×D3)⋊C4C2×D311yescharacteristic
195C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4C2×D311yescharacteristic, complemented
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—61no—
207C2×C4×Dic3C2×D311yescharacteristic, complemented
208#882—38no—
209C3×#95—21no—
210C3×#95—31no—
211C3×#95—31no—
212C3×#95C2×D311yescharacteristic, complemented
213C3×#95C2×D311yescharacteristic, complemented
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—31no—
220C3⋊#95—61no—
221C3⋊#95C2×D311yescharacteristic, complemented
222C3⋊#95C2×D311yescharacteristic, complemented
223C23×C32C2411yescharacteristic
224C22×C3⋊D3—21no—
225C22×C3⋊D3—21no—
226C22×C3⋊D3—21no—
227C22×C3⋊D3—21no—
228C22×C3⋊D3—21no—
229C22×C3⋊D3—21no—
230C22×C3⋊D3C22×C412yes—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3C22×C412yes—
250C22×C3×D3C22×C412yes—
251C22×C3×D3C22×C412yes—
252C2×D32—44no—
253C2×D32—44no—
254C2×D32—44no—
255C2×D32—44no—
256C2×D32—44no—
257C2×D32—44no—
258C2×D32—44no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4C22×C412yes—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C2×C3⋊Dic3—21no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276C2×C3⋊Dic3C22×C412yes—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3C22×C412yes—
292C3×D12—44no—
293C3×C4×D3—44no—
294#626—44no—
295#625—44no—
296C2×#120—91no—
297#390—91no—
298#390—91no—
299#390—91no—
300#388—31no—
301#388—91no—
302#388—91no—
303#388—91no—
304#388—91no—
305#388—91no—
306#386—31no—
307#386—91no—
308#386—91no—
309#379—91no—
310#379—91no—
311C24×C3—31no—
312C24×C3—31no—
313C24×C3—31no—
314C23×D3—31no—
315C23×D3—31no—
316C23×D3—34no—
317C23×D3—34no—
318C23×D3—61no—
319C23×D3—121no—
320C23×D3—121no—
321C23×D3—121no—
322C23×D3—121no—
323C23×D3—121no—
324C23×D3—121no—
325C23×D3—121no—
326C23×D3—121no—
327C23×D3—121no—
328C23×D3—121no—
329C23×D3—121no—
330C23×D3—121no—
331C23×D3C22×D311yescharacteristic
332C23×D3C22×D311yescharacteristic
333C23×D3C22×D311yescharacteristic
334C2×C3×D4—34no—
335C2×C3×D4—121no—
336C2×C3×D4—121no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—121no—
346C22×C3×C4—121no—
347C22×C3×C4—121no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—121no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—121no—
361C2×#67—121no—
362C2×#67—121no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3C22×D311yescharacteristic
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C2×D12—34no—
378C2×D12—41no—
379C2×D12—41no—
380C2×D12—121no—
381C2×D12—121no—
382C2×D12C4×D314yes—
383C2×C4×D3—41no—
384C2×C4×D3—41no—
385C2×C4×D3—41no—
386C3×C4⋊C4—121no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—121no—
389C3×C22⋊C4—121no—
390C3×C22⋊C4—121no—
391C3×C22⋊C4—121no—
392C3×C22⋊C4—121no—
393C3×C42—121no—
394#217—34no—
395#217—121no—
396#217—121no—
397#217—121no—
398#217—121no—
399#217—121no—
400#217—121no—
401(C2×D3)⋊C4—34no—
402(C2×D3)⋊C4—34no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—41no—
405(C2×D3)⋊C4—41no—
406(C2×D3)⋊C4—41no—
407(C2×D3)⋊C4—41no—
408(C2×D3)⋊C4—41no—
409(C2×D3)⋊C4—64no—
410(C2×D3)⋊C4—121no—
411(C2×D3)⋊C4—121no—
412(C2×D3)⋊C4—121no—
413(C2×D3)⋊C4—121no—
414(C2×D3)⋊C4—121no—
415(C2×D3)⋊C4—121no—
416(C2×D3)⋊C4—121no—
417(C2×D3)⋊C4—121no—
418(C2×D3)⋊C4—122no—
419(C2×D3)⋊C4—121no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4—121no—
422(C2×D3)⋊C4—121no—
423(C2×D3)⋊C4—121no—
424(C2×D3)⋊C4—121no—
425(C2×D3)⋊C4—122no—
426(C2×D3)⋊C4C4×D314yescomplemented
427C4⋊Dic3—121no—
428C4⋊Dic3—121no—
429C4⋊Dic3—122no—
430Dic3⋊C4—41no—
431Dic3⋊C4—121no—
432Dic3⋊C4—121no—
433C4×Dic3—41no—
434C4×Dic3—121no—
435C4×Dic3—121no—
436C4×Dic3—121no—
437C4×Dic3—121no—
438C4×Dic3—122no—
439C22×C32C23×C411yescharacteristic
440C22×C32H(5,𝔽2)11yescharacteristic
441C22×C32H(5,𝔽2)11yescharacteristic
442C22×C32H(5,𝔽2)11yescharacteristic
443C22×C32H(5,𝔽2)11yescharacteristic
444C22×C32H(5,𝔽2)11yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—22no—
457C2×C3×D3—22no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—22no—
461C2×C3×D3—22no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474D32—416no—
475C32×C4—22no—
476C32×C4—41no—
477C32×C4—41no—
478C3⋊Dic3—22no—
479C3⋊Dic3—41no—
480C3⋊Dic3—41no—
481C3×Dic3—22no—
482C3×Dic3—41no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C3×Dic3—41no—
486C25—91no—
487C22×D4—31no—
488C22×D4—91no—
489C22×D4—91no—
490C23×C4—31no—
491#120—98no—
492C2×C4⋊C4—31no—
493C2×C4⋊C4—91no—
494C2×C4⋊C4—91no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—31no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C22⋊C4—91no—
507C2×C22⋊C4—91no—
508C2×C22⋊C4—91no—
509C2×C22⋊C4—91no—
510C2×C22⋊C4—91no—
511C2×C22⋊C4—91no—
512C2×C22⋊C4—91no—
513C2×C42—31no—
514C2×C42—91no—
515C2×C42—91no—
516#95—31no—
517#95—31no—
518#95—91no—
519#95—91no—
520#95—91no—
521#95D3211yescharacteristic, complemented
522C23×C3—21no—
523C23×C3—32no—
524C23×C3—32no—
525C23×C3—32no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3—61no—
535C23×C3—61no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3C23×D311yescharacteristic
545C23×C3C23×D311yescharacteristic
546C22×D3—21no—
547C22×D3—21no—
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3—32no—
565C22×D3—32no—
566C22×D3—62no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—61no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—61no—
576C22×D3—61no—
577C22×D3—61no—
578C22×D3—61no—
579C22×D3—121no—
580C22×D3—121no—
581C22×D3—121no—
582C22×D3—121no—
583C22×D3—121no—
584C22×D3—121no—
585C22×D3—124no—
586C22×D3—124no—
587C22×D3—124no—
588C22×D3—124no—
589C22×D3—124no—
590C22×D3—124no—
591C22×D3—124no—
592C22×D3—124no—
593C22×D3—124no—
594C22×D3—124no—
595C22×D3—124no—
596C22×D3—124no—
597C22×D3—124no—
598C22×D3—124no—
599C22×D3C2×C4×D312yes—
600C22×D3C2×C4×D312yes—
601C22×D3C2×C4×D312yes—
602C3×D4—124no—
603C2×C3×C4—21no—
604C2×C3×C4—21no—
605C2×C3×C4—21no—
606C2×C3×C4—21no—
607C2×C3×C4—22no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—22no—
621C2×C3×C4—32no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—61no—
630C2×C3×C4—61no—
631C2×C3×C4—61no—
632C2×C3×C4—61no—
633C2×C3×C4—61no—
634C2×C3×C4—61no—
635C2×C3×C4—61no—
636C2×C3×C4—61no—
637C2×C3×C4—61no—
638C2×C3×C4—61no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—124no—
644C2×C3×C4C2×C4×D312yes—
645C2×C3×C4C2×C4×D312yes—
646#67—124no—
647#67—124no—
648#67—124no—
649C2×Dic3—21no—
650C2×Dic3—21no—
651C2×Dic3—21no—
652C2×Dic3—21no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—21no—
662C2×Dic3—21no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—62no—
666C2×Dic3—61no—
667C2×Dic3—61no—
668C2×Dic3—61no—
669C2×Dic3—61no—
670C2×Dic3—62no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—61no—
675C2×Dic3—61no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—61no—
681C2×Dic3—61no—
682C2×Dic3—61no—
683C2×Dic3—121no—
684C2×Dic3—121no—
685C2×Dic3—121no—
686C2×Dic3—121no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—121no—
690C2×Dic3C2×C4×D312yes—
691D12—44no—
692D12—124no—
693C4×D3—44no—
694C2×C32#51811yescharacteristic
695C2×C32#51811yescharacteristic
696C2×C32#51811yescharacteristic
697C2×C32#56011yescharacteristic
698C2×C32#56011yescharacteristic
699C2×C32#56011yescharacteristic
700C2×C32H(3,𝔽4)11yescharacteristic
701C3⋊D3—42no—
702C3×D3—42no—
703C3×D3—42no—
704C3×D3—42no—
705C24—31no—
706C24—31no—
707C24—31no—
708C24—94no—
709C24—91no—
710C24—361no—
711C24—361no—
712C24—361no—
713C24—361no—
714C24—361no—
715C24—361no—
716C2×D4—34no—
717C2×D4—94no—
718C2×D4—94no—
719C2×D4—121no—
720C2×D4—121no—
721C2×D4—361no—
722C2×D4—361no—
723C2×D4—361no—
724C2×D4—361no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—31no—
729C22×C4—31no—
730C22×C4—91no—
731C22×C4—91no—
732C22×C4—91no—
733C22×C4—121no—
734C22×C4—121no—
735C22×C4—121no—
736C22×C4C2×D3211yescharacteristic
737C22×C4C2×D3211yescharacteristic
738C22×C4C2×D3211yescharacteristic
739C4⋊C4—121no—
740C4⋊C4—361no—
741C4⋊C4—361no—
742C22⋊C4—34no—
743C22⋊C4—94no—
744C22⋊C4—94no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—121no—
748C22⋊C4—121no—
749C22⋊C4—121no—
750C22⋊C4—361no—
751C22⋊C4—361no—
752C22⋊C4—361no—
753C22⋊C4—361no—
754C22⋊C4—361no—
755C22⋊C4—361no—
756C22⋊C4—361no—
757C22⋊C4—361no—
758C22⋊C4—361no—
759C22⋊C4—361no—
760C42—121no—
761C42—361no—
762C42—361no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—62no—
771C22×C3—62no—
772C22×C3—62no—
773C22×C3—62no—
774C22×C3—62no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—121no—
780C22×C3—121no—
781C22×C3—121no—
782C22×C3—121no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3—121no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—121no—
791C22×C3C22×C4×D311yescharacteristic
792C22×C3C22×C4×D311yescharacteristic
793C22×C3#100411yescharacteristic
794C22×C3#100411yescharacteristic
795C22×C3#100411yescharacteristic
796C22×C3#100411yescharacteristic
797C22×C3#100411yescharacteristic
798C22×C3#100411yescharacteristic
799C22×C3#100911yescharacteristic
800C22×C3#100911yescharacteristic
801C22×C3#100911yescharacteristic
802C22×C3#100911yescharacteristic
803C22×C3#100911yescharacteristic
804C22×C3#100911yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—22no—
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—22no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—41no—
823C2×D3—41no—
824C2×D3—41no—
825C2×D3—41no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—122no—
833C2×D3—122no—
834C2×D3—122no—
835C2×D3—1216no—
836C2×D3—1216no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—121no—
840C2×D3—121no—
841C2×D3—121no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—241no—
846C2×D3—241no—
847C2×D3—241no—
848C2×D3—241no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—42no—
852C3×C4—42no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—41no—
856C3×C4—41no—
857C3×C4—62no—
858C3×C4—81no—
859C3×C4—121no—
860C3×C4—121no—
861C3×C4—121no—
862C3×C4—121no—
863Dic3—22no—
864Dic3—41no—
865Dic3—41no—
866Dic3—41no—
867Dic3—41no—
868Dic3—62no—
869Dic3—62no—
870Dic3—122no—
871Dic3—122no—
872Dic3—121no—
873Dic3—121no—
874Dic3—121no—
875Dic3—121no—
876Dic3—241no—
877C32#237511yescharacteristic, complemented, Sylow
878C23—32no—
879C23—32no—
880C23—32no—
881C23—61no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—61no—
889C23—61no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—92no—
900C23—181no—
901C23—181no—
902C23—181no—
903C23—181no—
904C23—181no—
905C23—181no—
906C23—364no—
907C23—364no—
908C23—364no—
909C23—364no—
910C23—364no—
911C23—364no—
912C23—364no—
913C23C22×D3211yescharacteristic
914D4—124no—
915D4—364no—
916D4—364no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—32no—
926C2×C4—61no—
927C2×C4—61no—
928C2×C4—61no—
929C2×C4—61no—
930C2×C4—61no—
931C2×C4—61no—
932C2×C4—61no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—92no—
941C2×C4—124no—
942C2×C4—181no—
943C2×C4—181no—
944C2×C4—181no—
945C2×C4—181no—
946C2×C4—181no—
947C2×C4—181no—
948C2×C4—181no—
949C2×C4—181no—
950C2×C4C4×D3212yes—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—21no—
955C2×C3—21no—
956C2×C3—21no—
957C2×C3—21no—
958C2×C3—122no—
959C2×C3—122no—
960C2×C3—122no—
961C2×C3#548611yescharacteristic
962C2×C3#552111yescharacteristic
963C2×C3#554511yescharacteristic
964C2×C3#554511yescharacteristic
965C2×C3#554511yescharacteristic
966C2×C3#554511yescharacteristic
967C2×C3#559411yescharacteristic
968C2×C3#562011yescharacteristic
969C2×C3#562011yescharacteristic
970C2×C3#562011yescharacteristic
971C2×C3#566611yescharacteristic
972C2×C3#566611yescharacteristic
973C2×C3#568311yescharacteristic
974C2×C3#571111yescharacteristic
975D3—42no—
976D3—42no—
977D3—42no—
978D3—122no—
979D3—122no—
980D3—242no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—62no—
986C22—62no—
987C22—62no—
988C22—62no—
989C22—62no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—121no—
996C22—121no—
997C22—121no—
998C22—121no—
999C22—121no—
1000C22—121no—
1001C22—121no—
1002C22—182no—
1003C22—182no—
1004C22—182no—
1005C22—3616no—
1006C22—361no—
1007C22—361no—
1008C22—361no—
1009C22—361no—
1010C22C2×C4×D3211yescharacteristic
1011C22#6430711yescharacteristic
1012C22#6430811yescharacteristic
1013C22#6431311yescharacteristic
1014C22#6431311yescharacteristic
1015C22#6431411yescharacteristic
1016C22#6432011yescharacteristic
1017C4—22no—
1018C4—41no—
1019C4—41no—
1020C4—62no—
1021C4—121no—
1022C4—121no—
1023C4—121no—
1024C4—121no—
1025C4—182no—
1026C4—361no—
1027C4—361no—
1028C3—21no—
1029C3#7488211yescharacteristic, complemented
1030C3#7584011yescharacteristic, complemented
1031C2—122no—
1032C2—122no—
1033C2—122no—
1034C2—362no—
1035C2#1059399411yescharacteristic
1036C2#1059425411yescharacteristic
1037C2#1059430911yescharacteristic
1038C2#1059431011yescharacteristic
1039C2#1059460611yescharacteristic
1040C2#1059466211yescharacteristic
1041C2#1059466311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenter#95D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10592369C2semidirect
3. C3×#4669C2semidirect
4. C3×#4665C2semidirect
5. #10591399C2semidirect
6. #10591399C2semidirect
7. #10591385C2semidirect
8. #10591384C2semidirect
9. #10591382C2semidirect
10. #10591381C2semidirect
11. #10591318C2semidirect
12. #10591316C2semidirect
13. #10591283C2semidirect
14. #10591282C2semidirect
15. #10591202C2semidirect
20. C22×C3×C4×D3C22semidirect
26. C2×C4⋊(C3⋊Dic3)C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
35. C2×C3×C4×Dic3C22semidirect
36. C2×#3724C22semidirect
44. C2×(C2×D3)⋊Dic3C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×Dic32C22semidirect
47. #63922C4semidirect
48. C32×#95C22semidirect
49. #63658C22semidirect
50. C3×C3⋊#95C22semidirect
51. C3×C3⋊#95C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
82. #4669D3semidirect
84. #4665D3semidirect
95. C22×D32C2×C4semidirect
121. #3752C2×C4semidirect
129. C3×(C2×D3)⋊C4C2×C4semidirect
141. (C2×D3)⋊Dic3C2×C4semidirect
153. C22×C4×D3C2×D3semidirect
195. C2×(C2×D3)⋊C4C2×D3semidirect
201. C2×Dic3⋊C4C2×D3semidirect
207. C2×C4×Dic3C2×D3semidirect
212. C3×#95C2×D3semidirect
213. C3×#95C2×D3semidirect
221. C3⋊#95C2×D3semidirect
222. C3⋊#95C2×D3semidirect
426. (C2×D3)⋊C4C4×D3semidirect
521. #95D32semidirect
877. C32#2375semidirect
1029. C3#74882semidirect
1030. C3#75840semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#639222
#105923692
C3×#46692
C3×#46652
#105913992
#105913852
#105913842
#105913822
#105913812
#105913182
#105913162
#105912832
#105912822
#105912022
#758403
#748823